Aleks 360 Access Card (18 Weeks) for Intermediate Algebra
4th Edition
ISBN: 9780077844462
Author: Julie Miller
Publisher: MCG
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Chapter R, Problem 44RE
For Exercises 44-45, answer may vary.
45. Write an example of the associative property of multiplication.
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Într-un bloc sunt apartamente cu 2 camere și apartamente cu 3 camere , în total 20 de apartamente și 45 de camere.Calculați câte apartamente sunt cu 2 camere și câte apartamente sunt cu 3 camere.
1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set
Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k
components, where k is the greatest common divisor of {n, r,s}.
Question 3
over a field K.
In this question, MË(K) denotes the set of n × n matrices
(a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is
equivalent to A-¹? Justify your answer.
(b) Let B be given by
8
B = 0 7 7
0 -7 7
Working over the field F2 with 2 elements, compute the rank of B as an element
of M2(F2).
(c) Let
1
C
-1 1
[4]
[6]
and consider C as an element of M3(Q). Determine the minimal polynomial
mc(x) and hence, or otherwise, show that C can not be diagonalised.
[7]
(d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write
down all the eigenvalues. Show your working.
[8]
Chapter R Solutions
Aleks 360 Access Card (18 Weeks) for Intermediate Algebra
Ch. R - Prob. 1RECh. R - Prob. 2RECh. R - For Exercises 2-3, answers may vary. 2. List three...Ch. R - For Exercises 4-9, write an expression in words...Ch. R - For Exercises 4-9, write an expression in words...Ch. R - For Exercises 4-9, write an expression in words...Ch. R - For Exercises 4-9, write an expression in words...Ch. R - For Exercises 4-9, write an expression in words...Ch. R - For Exercises 4-9, write an expression in words...Ch. R - For Exercises 10-12, graph each set and write the...
Ch. R - For Exercises 10-12, graph each set and write the...Ch. R - For Exercises 10-12, graph each set and write the...Ch. R - Prob. 13RECh. R - For Exercises 14-15, find the opposite,...Ch. R - Prob. 15RECh. R - Prob. 16RECh. R - For Exercises 16-17, simplify the exponents and...Ch. R - Prob. 18RECh. R - For Exercises 18-33, perform the indicated...Ch. R - For Exercises 18-33, perform the indicated...Ch. R - Prob. 21RECh. R - Prob. 22RECh. R - For Exercises 18-33, perform the indicated...Ch. R - Prob. 24RECh. R - For Exercises 18-33, perform the indicated...Ch. R - Prob. 26RECh. R - Prob. 27RECh. R - Prob. 28RECh. R - For Exercises 18-33, perform the indicated...Ch. R - Prob. 30RECh. R - For Exercises 18-33, perform the indicated...Ch. R - Prob. 32RECh. R - For Exercises 18-33, perform the indicated...Ch. R - Prob. 34RECh. R - Prob. 35RECh. R - Prob. 36RECh. R - For Exercises 36-39, apply the distributive...Ch. R - Prob. 38RECh. R - For Exercises 36-39, apply the distributive...Ch. R - Prob. 40RECh. R - Prob. 41RECh. R - Prob. 42RECh. R - Prob. 43RECh. R - For Exercises 44-45, answer may vary. 45. Write an...Ch. R - Prob. 45RECh. R - Prob. 1TCh. R - Write the opposite, reciprocal, and absolute value...Ch. R - Prob. 3TCh. R - Prob. 4TCh. R - Prob. 5TCh. R - For Exercises 5-6, graph the inequality and...Ch. R - For Exercises 7-8, write each English phrase as an...Ch. R - Prob. 8TCh. R - Prob. 9TCh. R - Prob. 10TCh. R - Prob. 11TCh. R - Prob. 12TCh. R - Prob. 13TCh. R - Prob. 14TCh. R - Prob. 15TCh. R - Prob. 16TCh. R - For Exercise 17-20, answer true or false. 17....Ch. R - Prob. 18TCh. R - Prob. 19TCh. R - For Exercise 17-20, answer true or false. 20....
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- R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]arrow_forwardQuestion 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]arrow_forwardpart b pleasearrow_forward
- Question 5 (a) Let a, b, c, d, e, ƒ Є K where K is a field. Suppose that the determinant of the matrix a cl |df equals 3 and the determinant of determinant of the matrix a+3b cl d+3e f ГЪ e [ c ] equals 2. Compute the [5] (b) Calculate the adjugate Adj (A) of the 2 × 2 matrix [1 2 A = over R. (c) Working over the field F3 with 3 elements, use row and column operations to put the matrix [6] 0123] A = 3210 into canonical form for equivalence and write down the canonical form. What is the rank of A as a matrix over F3? 4arrow_forwardQuestion 2 In this question, V = Q4 and - U = {(x, y, z, w) EV | x+y2w+ z = 0}, W = {(x, y, z, w) € V | x − 2y + w − z = 0}, Z = {(x, y, z, w) € V | xyzw = 0}. (a) Determine which of U, W, Z are subspaces of V. Justify your answers. (b) Show that UW is a subspace of V and determine its dimension. (c) Is VU+W? Is V = UW? Justify your answers. [10] [7] '00'arrow_forwardTools Sign in Different masses and Indicated velocities Rotational inert > C C Chegg 39. The balls shown have different masses and speeds. Rank the following from greatest to least: 2.0 m/s 8.5 m/s 9.0 m/s 12.0 m/s 1.0 kg A 1.2 kg B 0.8 kg C 5.0 kg D C a. The momenta b. The impulses needed to stop the balls Solved 39. The balls shown have different masses and speeds. | Chegg.com Images may be subject to copyright. Learn More Share H Save Visit > quizlet.com%2FBoyE3qwOAUqXvw95Fgh5Rw.jpg&imgrefurl=https%3A%2F%2Fquizlet.com%2F529359992%2Fc. Xarrow_forward
- 2. What is the total length of the shortest path that goes from (0,4) to a point on the x-axis, then to a point on the line y = 6, then to (18.4)?arrow_forwardموضوع الدرس Prove that Determine the following groups Homz(QZ) Hom = (Q13,Z) Homz(Q), Hom/z/nZ, Qt for neN- (2) Every factor group of adivisible group is divisble. • If R is a Skew ficald (aring with identity and each non Zero element is invertible then every R-module is free.arrow_forwardI have ai answers but incorrectarrow_forward
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